On cross t-intersecting families of sets

For all p, t with 0 < p < 0.11 and 1 ⩽ t ⩽ 1 / ( 2 p ) , there exists n 0 such that for all n, k with n > n 0 and k / n = p the following holds: if A and B are k-uniform families on n vertices, and | A ∩ B | ⩾ t holds for all A ∈ A and B ∈ B , then | A | | B | ⩽ ( n − t k − t ) 2 .